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A003641 Number of genera of imaginary quadratic field with discriminant -k, k = A039957(n).
(Formerly M0061)
3
1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 2, 2, 2, 2, 1, 1, 1, 2, 1, 2, 2, 1, 1, 1, 2, 2, 1, 4, 1, 2, 1, 2, 2, 1, 1, 4, 2, 1, 2, 1, 4, 2, 1, 2, 1, 1, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 2, 2, 4, 2, 2, 2, 2, 1, 2, 1, 4, 1, 1, 2, 2, 4, 1, 1, 2, 1, 4, 1, 1, 1, 1, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

In other words, this is the number of genera of those imaginary quadratic fields that have a discriminant which is odd and fundamental. The discriminant will be squarefree and of the form -4n+1. - Andrew Howroyd, Jul 25 2018

REFERENCES

D. A. Buell, Binary Quadratic Forms. Springer-Verlag, NY, 1989, pp. 224-241.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Table of n, a(n) for n=1..105.

Index entries for sequences related to quadratic fields

FORMULA

a(n) = 2^(omega(A039957(n)) - 1). - Jianing Song, Jul 24 2018

EXAMPLE

a(4) = 2 because -15 = -A039957(4) and the number of genera of the quadratic field with discriminant -15 is 2. - Andrew Howroyd, Jul 25 2018

MATHEMATICA

2^(PrimeNu[Select[Range[1000], Mod[#, 4] == 3 && SquareFreeQ[#]&]] - 1) (* Jean-Fran├žois Alcover, Jul 25 2019, after Andrew Howroyd *)

PROG

(PARI) for(n=1, 1000, if(n%4==3 && issquarefree(n), print1(2^(omega(n) - 1), ", "))) \\ Andrew Howroyd, Jul 24 2018

CROSSREFS

Cf. A001221 (omega), A003640, A003642, A039957.

Sequence in context: A317934 A279848 A001826 * A165190 A025890 A316975

Adjacent sequences:  A003638 A003639 A003640 * A003642 A003643 A003644

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Mira Bernstein

EXTENSIONS

Name clarified by Jianing Song, Jul 24 2018

STATUS

approved

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Last modified December 7 05:14 EST 2019. Contains 329839 sequences. (Running on oeis4.)